PRL 96, 177801 (2006)
PHYSICAL REVIEW LETTERS
week ending
5 MAY 2006
Structure and Dynamics of Liquid Crystalline Pattern Formation in Drying Droplets of DNA
Ivan I. Smalyukh,1,2 Olena V. Zribi,1 John C. Butler,1 Oleg D. Lavrentovich,2 and Gerard C. L. Wong1,*
1
Department of Physics, Department of Materials Science and Engineering, Department of Bioengineering,
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
2
Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242, USA
(Received 1 January 2006; published 2 May 2006)
We investigate the formation of ringlike deposits in drying drops of DNA. In analogy with the colloidal
‘‘coffee rings,’’ DNA is transported to the perimeter by the capillary flow. At the droplet edge, however,
DNA forms a lyotropic liquid crystal (LC) with concentric chain orientations to minimize the LC elastic
energy. During the final stages of drying, the contact line retracts, and the radial stress causes undulations
at the rim that propagate inward through the LC and form a periodic zigzag structure. We examine the
phenomenon in terms of a simple model based on LC elasticity.
DOI: 10.1103/PhysRevLett.96.177801
PACS numbers: 61.30.Pq, 61.30.Vx, 81.16.Fg, 87.14.Gg
Drying droplets of colloidal suspensions form ‘‘coffee
ring’’ stains due to the capillary flow caused by contact line
(CL) pinning [1]. This phenomenon has been used for the
assembly of nanoparticles [2,3] and diblock copolymers
[4]. For gene expression profiling, an array of DNA droplets is often dried on a glass surface for hybridization
studies [5]. Since DNA can be stretched by flow [6–9]
and ‘‘molecular combing’’ [10], single DNA chains usually
align perpendicular to the CL of a drying drop. In this
Letter, we show that, when a concentrated DNA droplet is
dried, a coffee ring stain is also formed, but, contrary to
intuition, the extended DNA chains trace out zigzags along
the CL and form a periodic pattern (Fig. 1). During most of
the drying time, the contact line is pinned, and DNA chains
from the droplet interior are transported to the perimeter.
At the droplet edge, a lyotropic liquid crystal (LC) is
formed, in which DNA chains align along the droplet
edge to minimize LC elastic and surface anchoring energies. During the final stages of drying, the CL retracts, and
radial dilative stress causes undulations at the rim that
propagate inward through the elastic LC medium, giving
rise to the domain pattern. A simple model based on LC
elasticity explains the observations.
The experiments are conducted using -DNA (contour
length lc 16:3 m, 48 502 bp, persistence length lp 50 nm), obtained from New England BioLabs, Inc. The
pattern is observed for a broad range of initial DNA concentrations Ci 0:02–5 mg=ml, initial droplet volumes
Vi 1–50 l, and for surfaces with different hydrophilicity (clean glass plates, SiO, and indium tin oxide coatings, etc.; contact angle 15 110 ). The droplet’s
radius R 0:5–12 mm is varied by changing Vi and .
The pattern consists of the herringbonelike domains with a
self-similar periodic structure (Fig. 1). The periodicity L
and deposit thickness d increase with Vi and Ci ; in the
deposits, L is a monotonously increasing function of d
[Fig. 1(a)], measured using confocal microscopy vertical
cross sections [Fig. 1(f)]. For example, L can be varied
from L < lc to L > lc and d from submicron to tens of
0031-9007=06=96(17)=177801(4)
microns by changing Vi 1–50 l [Fig. 1(a)]. For DNA
rings of d < 10 m obtained with droplets of Vi < 30 l
at 1 mg=ml of DNA, the polarizing microscopy (PM)
textures appear gray [Fig. 1(c)]. PM images are polychromatic if Vi 30 l [Fig. 1(d)], indicating that, for wavelengths in the visible spectral range, nd , where
n ne n0 and ne ; n0 are extraordinary and ordinary
refractive indices. We estimate n by correlating texture
colors and the measured d: n 0:011 0:004 for a
FIG. 1 (color). DNA pattern at the perimeter of a dried drop:
(a) periodicity L vs thickness d in the central thickest part of the
ring [obtained by varying Vi 1–50 l]; the inset shows a
typical birefringent ring; (b) PM texture of the pattern colocalized with the fluorescence signal from a small number of molecules marked by YOYO-1; (c) –(e) PM textures of the pattern
inside (c) a thin (<10 m) ring and (d),(e) a thick (>20 m)
ring obtained (c),(d) without and (e) with a 530 nm retardation
plate; (f) a vertical confocal microscopy cross section (all DNA
labeled) showing the bell-shaped profile of the ring. The crossed
polarizer and analyzer are parallel to the vertical and horizontal
directions in the plane of the images in (a) –(e), and the retardation plate is at 45 to them in (e). The CL is on the right side of
the ring fragments in (b)–(f).
177801-1
© 2006 The American Physical Society
PRL 96, 177801 (2006)
PHYSICAL REVIEW LETTERS
dried film of -DNA (n < 0 because of the conjugated
bonds in base pairs) and even smaller in the lyotropic LC
observed during drying. Droplets of Vi < 1 l, such as
those in DNA chips, also produce ringlike deposits, but the
pattern is barely observable in PM because nd is small.
The PM texture of the pattern (Fig. 1) changes upon
rotation of the sample; each part can be brought to extinction at a well-defined orientation with respect to the
crossed polarizers. This indicates that the director n^ (average local orientation of DNA chains) is not twisted along
the normal to the substrate, in agreement with the theoretical predictions [11] that twist is suppressed with increasing
the polymer contour length and in phases with positional
order. When the sample is rotated in the presence of a
530 nm retardation plate between crossed polarizers, continuous changes of alternating blue and orange bands are
observed [Fig. 1(e)]. This allows one to deduce the
^ The result agrees well
thickness-averaged in-plane n.
with the fluorescence signal from the dyed DNA molecules
within unlabeled DNA [12] colocalized with the PM texture [Fig. 1(b)]: The extended DNA and n^ are uniformly
oriented at 30 –45 to the CL within the stripes and the
in-plane n^ traces out zigzags from stripe to stripe.
^ y; z, we use
In order to elucidate the 3D structure of nx;
fluorescence confocal polarizing microscopy (FCPM) [13]
and stain the DNA with acridine orange dye (AO, Aldrich
Chemical Co.), which intercalates parallel to the base pairs
[14], i.e., approximately perpendicular to the DNA axis
(Fig. 2). When studied with polarized FCPM light, the spatial pattern of fluorescence signal visualizes the director
structure [15]. To resolve n^ across the film thickness, we
study thick, d 20–50 m, deposit rings obtained after
drying of droplets of Vi 50 l at 1–2 mg=ml of DNA.
The FCPM resolution (1 m) is sufficient to resolve the
structure of n^ in 3D: The pattern is composed of stripes
with essentially thickness-independent periodically alternating n^ parallel to the substrate and at 45 –60 to the
radial direction (Fig. 2). The vertical wall defects run
across the whole thickness of the ring [Figs. 2(e)–2(h)]
and are due to the discontinuous jumps of n^ between the
stripes.
To get insights into the physics of this phenomenon, we
experimentally study dynamics of the droplet drying. At
the initial stages, it resembles coffee ring formation [1]. As
long as the CL is pinned (Fig. 3), the evaporation flux is the
strongest next to the edge of the drop. As evidenced by
tracking fluorescently labeled tracer DNA, the solute flows
from the drop interior toward the periphery to compensate
the evaporation losses. This radial outward flow transports
random-coiled DNA (1 m globules) to the drop’s perimeter. DNA concentration at the perimeter and the local
effective viscosity gradually increase so that DNA
Brownian motion is hindered (as observed by tracking
fluorescently dyed molecules). The Stokes drag becomes
strong enough to extend DNA [7–9], driving the LC self-
week ending
5 MAY 2006
FIG. 2 (color). (a),(b) In-plane and (c),(d) vertical FCPM cross
sections of the director structure in a relatively thin ring;
(e),(f) vertical FCPM cross sections obtained for a thick ring
illustrating that orientation of n^ across the film thickness is the
same within the stripes; (g) schematics of DNA orientation
(visualized by cylinders) in domains with n^ at 45 to the
radial direction and the vertical wall defect (shaded plane) in
between; (h) a typical FCPM vertical cross section of a thick ring
(FCPM polarization along the local CL) visualizes the wall
defect separating domains with nearly orthogonal n;
^ (i) FCPM
intensity scale. The polarization of the FCPM probing light is at
45 with respect to the radial direction in (a),(c),(e) and at 45
in (b),(d),(f).
organization at the droplet rim [16]. The drop at this stage
has a birefringent wedge-shaped LC ring with n^ parallel to
the CL, which is still pinned at the initial location. The
DNA alignment parallel to the drop’s edge is counterintuitive because DNA is expected to extend along the flow [7–
9], which is mainly in the radial direction. To understand
these experimental observations, we consider the LC surface anchoring and bulk elastic properties [11,16–21].
Although long DNA chains usually have random coil conformations, it has been demonstrated that ‘‘molecular
crowding’’ can straighten the random coils and lead to
LC phases [16]. The macroscopic elasticity can be described in a framework similar to other polymer LCs
composed of long flexible chains [11,16–21]. The elastic
distortions of the LC director n^ are associated with free
energy density [20,21]:
f
K1
K
^ 2 2 n^ r n
^ 2
r n
2
2
K
E p
^ 2
3 n^ r n
:
2 0p
2
(1)
Here K1 , K2 , and K3 are Frank elastic constants for splay,
^ respectively, p is
twist, and bend deformations of n,
variation of the local polymer density, 0p is the mean
polymer density, and E is the osmotic compressibility
177801-2
PRL 96, 177801 (2006)
PHYSICAL REVIEW LETTERS
modulus. As compared to the small-molecule LCs, the
fundamental difference is that K1 K2 ; K3 and that there
is a free energy cost for locally compressing/dilating the
LC composed of long flexible chains, described by the last
term in (1).
We determined that the droplet-air and droplet-substrate
interfaces impose tangential boundary conditions, setting n^
parallel to these interfaces [22]. Satisfying these conditions, the radial structure of n^ would then require splay
^ In the limit of small and for typical
deformations of n.
widths of the LC wedge R R=10 [23], the associated
elastic energy of the LC wedge at the perimeter is Fradial 10K1 R. In contrast, the concentric structure with
DNA along the CL involves bend deformations of n^ at
the large length scales R; the elastic energy is Fconc K3 fR lnR=R R Rg [23]. For typical R and
R, one obtains Fconc =Fradial 104 K3 =K1 1; since
K3 K1 , Fconc is much smaller than Fradial . This explains
the concentric n^ (Figs. 3 and 4) that can persist until the end
of drying and leave a deposit with annular DNA alignment
if the CL does not recede (observed at Ci > 15 mg=ml for
-DNA [23] or at even higher Ci for shorter DNA fragments [24]). The droplets with smaller Ci form a pattern
^
that is a periodic distortion of the initial concentric n.
The contact angle varies due to evaporative water
losses and slight decrease of surface tension [25]. When
2 –4 , the CL is depinned and recedes [Figs. 3(a)–
3(f)], similar to drops of other complex fluids [26]. The
imposed stress and reverse (inward) radial flow pull the
^
extended DNA in the radial direction [10], i.e., normal to n.
At very small Ci , the shrinking droplet with receding CL
can stretch the single biopolymer molecule in the radial
direction [6,10,27]. In our case of relatively large Ci , DNA
molecules are extended along the CL and form an LC
week ending
5 MAY 2006
phase before the CL depinning. The minimum of LC
^ hence,
elastic free energy corresponds to the concentric n;
the radial dilative stress in the vicinity of the receding CL
competes with the LC elasticity, resulting in a periodic
distortions of n^ [Figs. 1, 2, and 3(g)]. Formed wavy undulations are reminiscent of the undulations induced by a
dilative mechanical stress in columnar LCs [17,28]. At the
onset of pattern formation, the distortions first appear next
to the CL [Figs. 3(g) and 3(h)] and then expand to the
^ The ripples of n^
whole width of the ring with concentric n.
at the CL propagate in the radial direction nr / cosqx p
expq2 r K3 =E q2 K1 and decay at the characteristic
p
length lr q2 E q2 K1 =K3 [Figs. 3(g) and 3(h)],
where q 2=L; this is analogous to the response of a
polymer nematic to a grooved surface [21]. For experip
mental L 3–150 m and typical K3 =E 5–10 nm
[21], E q2 K1 , one obtains lr 10–10 000 m, depending on L. This explains why the ripples of n^ occurring
at the CL penetrate deep into the LC ring [Figs. 3(g) and
3(h)]. The periodic stripes eventually run across the whole
width R of the birefringent ring and act as a ‘‘template’’
for the deposition of remaining DNA. When the remaining
water evaporates, solidification of the DNA deposit is
followed by formation of defect walls and cracks, evidenced by additional sharp lines (Fig. 1) that are typical
for phases with positional order. Interestingly, the final
structure and the pattern of DNA orientation (Figs. 1, 2,
and 4) resemble the ‘‘sawtooth-type’’ buckling instability
observed at high applied stresses in LCs with partial positional order [17,28]. The sequence of pattern formation and
the final director structure are summarized in Fig. 4.
In summary, we describe the periodic pattern formed in
the coffee rings of DNA drops and explain it in terms of a
FIG. 3 (color). (a) –(e) Vertical cross
sections showing drying droplet profile
with (a) the CL pinned and (b)–
(e) slowly receding (DNA stained with
AO dye); (f) profiles of the liquid-air
interface for different drying times, obtained from the cross sections similar to
(a) –(e); (g) PM texture and (h) a schematic illustration showing that the periodic distortion of originally concentric n^
starts at the CL and propagates towards
the droplet’s center. The crossed polarizer and analyzer in (g) are at 30 to the
vertical and horizontal directions of the
PM image.
177801-3
PRL 96, 177801 (2006)
PHYSICAL REVIEW LETTERS
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
FIG. 4 (color). The sequence of pattern formation: (a) The CL
is pinned and DNA is homogeneously distributed; (b) the CL is
still pinned but most of the molecules have already been brought
to the perimeter, stretched, and form the LC with n^ along the
edge; (c) CL is receding and the initially concentric n^ undergoes
undulations; (d),(e) when the drying process is complete, the
DNA deposit is a bell-shaped ring (d) with the DNA zigzag
pattern visualized in (e) via fluorescence from a small number of
molecules stained by YOYO-1; (f) schematics of the pattern.
[13]
simple model based on the LC nature of the ring at the
drying droplet edge. Similar phenomena are observed for
other semiflexible biopolymers [23,29]. Questions related
to details of the pattern formation remain, such as the
precise mechanism of wavelength selection and the relative role of the capillary flow in the LC with viscosity
coefficient anisotropy [30], as well as convection [9] and
Marangoni flows [26], which modify the pattern formation
at the late stages of the drying process. Since essentially all
the DNA is concentrated in a narrow ring threaded by a
network of defect walls with almost no DNA in the rest of
the stain, these effects should be accounted for in the
design of microarrays in which DNA droplets are sequentially deposited onto a surface for hybridization studies [5].
Without optimization of the wetting conditions, it is possible to damage the DNA chains or ‘‘miss’’ all the DNA in
the ring stain of a dried droplet even if perfect center-ofmass droplet alignment is achieved.
We acknowledge discussions with J. Freund, S. Garoff,
R. Larson, C. R. Safinya, J. Selinger, and J. Tang. This
work was supported by the Institute for Complex and
Adaptive Matter, the NSF Nanoscience and Engineering
Initiative (UIUC), and the NSF Grants No. DMR-0504516
(KSU) and DMR-0409769 (UIUC).
[16]
[17]
*Corresponding author.
Electronic address: gclwong@uiuc.edu
[1] R. D. Deegan et al., Nature (London) 389, 827 (1997).
[2] E. R. Dufresne et al., Phys. Rev. Lett. 91, 224501 (2003).
[3] V. V. Tsukruk, H. Ko, and S. Peleshanko, Phys. Rev. Lett.
92, 065502 (2004).
[14]
[15]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
177801-4
week ending
5 MAY 2006
M. Kimura et al., Langmuir 19, 9910 (2003).
M. C. Pirrung, Angew. Chem., Int. Ed. 41, 1276 (2002).
M. Chopra et al., J. Rheol. (N.Y.) 47, 1111 (2003).
J. F. Marko and E. D. Siggia, Science 265, 506 (1994).
T. T. Perkins, D. E. Smith, and S. Chu, Science 276, 2016
(1997).
S. S. Abramchuk et al., Europhys. Lett. 55, 294 (2001).
A. Bensimon et al., Science 265, 2096 (1994); D. Bensimon et al., Phys. Rev. Lett. 74, 4754 (1995).
R. D. Kamien and J. Toner, Phys. Rev. Lett. 74, 3181
(1995).
We labeled 1=10 000 DNA chains with dye YOYO-1
(Molecular Probes, 488 nm Ar-laser excitation and 510 –
550 nm fluorescence detection) so that there is one
YOYO-1 molecule per 15 bp of DNA.
I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich,
Chem. Phys. Lett. 336, 88 (2001).
L. S. Lerman, Proc. Natl. Acad. Sci. U.S.A. 49, 94
(1963).
AO dye (488 nm excitation and 510–550 nm detection) is
doped at 103 –104 wt: % into a 1 mg=ml aqueous
DNA solution. In the used epifluorescence mode, the
strongest signal corresponds to the FCPM polarization
perpendicular to n^ and the weakest signal when it is
^ Obtaining fluorescence textures for different
parallel to n.
polarizations, we extract n^ [13].
R. Podgornik et al., Biophys. Chem. 57, 111 (1995).
F. Livolant and A. Leforeestier, Prog. Polym. Sci. 21, 1115
(1996).
H. H. Strey, V. A. Parsegian, and R. Podgornik, Phys.
Rev. E 59, 999 (1999).
J. V. Selinger and R. F. Bruinsma, Phys. Rev. A 43, 2910
(1991); 43, 2922 (1991).
P. G. de Gennes, Mol. Cryst. Liq. Cryst. 34, 177 (1977).
A. Ciferri, W. R. Krigbaum, and R. B. Meyer, Polymer
Liquid Crystals (Academic, New York, 1982).
Using FCPM and fluorescence imaging of single dyed
DNA within unlabeled DNA molecules, we found that
both the droplet-air interface and the solid substrates
impose tangential boundary conditions on n^ at the interfaces. This implies that the surface anchoring energy is
minimized for tangential n^ (consistent with Meyer’s entropy considerations for long chains at the surfaces with
no chemical binding [21]). DNA orientation at the air
interface was additionally confirmed by visualizing n^
structures around air bubbles injected into the DNA LC.
O. Zribi et al. (to be published).
N. Morii et al., Biomacromolecules 5, 2297 (2004);
Biopolymers 77, 163 (2005).
T. Okubo and K. Koboyashi, J. Colloid Interface Sci. 205,
433 (1998).
R. D. Deegan, Phys. Rev. E 61, 475 (2000); V. N. Truskett
and K. J. Stebe, Langmuir 19, 8271 (2003); Phys. Rev.
Lett. 88, 164501 (2002).
H. Yokota et al., Nucleic Acids Res. 25, 1064 (1997).
P. Oswald et al., J. Phys. II (France) 6, 281 (1996).
L. Vonna et al., Langmuir 21, 9635 (2005).
R. G. Larson, J. Rheol. (N.Y.) 37, 175 (1993); F. Livolant,
J. Phys. (Paris) 48, 1051 (1987).